I’m looking for a one-way accumulator which can safely add new members (deletion is not necessary) and does not rely on a trusted party in any way. I’ve been looking for one, I need it for this project of mine. Unfortunately it appears that it does not exist yet.

My project has an authentication based on a block chain (like bitcoin) so it's manually initialized and after that it runs on it's own. If I put a hash in every block, nodes relay special packets only for the authenticated users, hence the need for a simple authentication scheme without a group manager, no one is to be trusted more then yourself in his honesty. After a round of votes all the nodes agree on the entrance of a new member and the hash is changed accordingly (or witnesses depending on the scheme) and the ban of a member is simply another "black list" hash (or some other method depending on the scheme).

Did you try Google @gurghet? Yes, there are. There are three existing schemes that immediately come to my mind. Two of them can even be made universal (non-membership witnesses). The question as it is is a pure reference request and off topic. If you have more concrete questions to an accumulator scheme, edit your question and I'll answer.
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DrLecterMar 19 '14 at 7:04

Just for the setup. But in a real world setting you will need soneone who runs the setup in any scheme @gurghet. Maybe you could edit your question and outline your application. Otherwise this seems to be a crystal ball thing ;)
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DrLecterMar 19 '14 at 9:57

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If you only want to add elements to the accumulator, then you can forget the factorization after setup @gurghet. However, if you want collision-freeness you can only accumulate prime numbers. But you can use the mapping to primes proposed in Appendix B of this paper for this purpose and thus accumulate arbitrary elements which you map to primes.
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DrLecterMar 19 '14 at 10:22

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@CodesInChaos Yes I know. The problem is that all dynamic accumulators have some secret that is generated during setup but could then be thrown away if you do not need to delete from the accumulator :/
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DrLecterMar 19 '14 at 14:13